The present invention concerns a method of simulating a shaping process or a sub-process of the shaping process.
States of objects involved in the shaping process, in particular a shaping machine, a shaping tool, and/or a material to be processed, are calculated in discrete and successive time steps with presetting of conditions, wherein the conditions represent input parameters of the shaping process.
Shaping machines are, for example, injection molding machines, injection presses, presses and the like. Shaping processes similarly follow that terminology.
The conditions represent the input parameters to the effect that they are the mathematical counterparts to the input parameters which are set for example by operators at the shaping machine. For example, in an injection molding process, input parameters could be parameters in relation to an injection profile. In the simulation then, for example, the machine elements which implement the injection profile could be simulated in detailed fashion. The parameters in relation to the injection profile then clearly establish the conditions which arise out of the parameters to the simulation. Instead of such an identical establishment of the conditions the conditions of the simulation can also be adapted to the input parameters by modeling of the actual facts. In the previous example with the injection profile that could be a time-dependent mass flow in the sprue. That is, of course, to be viewed purely by way of example. A similar situation applies for all input parameters or conditions.
The input parameters concern predominantly the motion and force profiles of drives of the shaping machine and other components of the shaping machine, that are to be controlled. Taking the example of an injection molding machine, those components would be, for example, drives for opening and closing a mold tool, producing a closing force, injection, post-pressure, ejector, heating means and so forth.
Hereinafter, the state of the art is described by reference to the example of injection molding machines (IMM). The conclusions also similarly apply to other shaping processes (injection molding processes are abbreviated as IM processes).
Simulations by means of finite element methods are highly processing-intensive and therefore require particularly powerful computing systems or a great deal of time. Depending on the duration and time discretization of the IM process or the magnitude and the spatial discretization of the geometries to be simulated, processing times of between some hours and several days are to be expected per filling operation on commercially usual computers.
Optimization tasks generally require implementation of a relatively large number of individual simulations. In order to arrive at a result in the optimization procedure as quickly as possible in a given computing system methods are necessary for very substantially reducing the computing involvement.
In practice, methods of statistical experiment planning (English: Design of Experiments—DoE) have become established. With a given number of parameters to be investigated, the methods serve to reduce the number of necessary experiments to such an extent that relevant interactions between the parameters and quality features can nonetheless be ascertained as accurately as possible.
Injection Molding Simulations
Numerical flow mechanics (computational fluid dynamics—CFD) can be used to simulate injection molding processes. In that respect, various kinds of filling simulations are in circulation (see Zheng R., Tanner R. I., Fan X.-J. (2012): Injection Molding. Heidelberg: Springer. Pages 111-147; Zhou H. (editor) (2013): Computer Modeling for Injection Molding. Hoboken: Wiley. Pages 49-254). They basically differ in their structure and the physics which they cover. Simulations commonly involve spatial and temporal discretization. In general, the fineness of the discretization determines the accuracy of the results and at the same time the required computing resources (size of the computing system and duration of the calculations).
A given product, that is to say the cavity of an injection molding tool, mostly occurs as CAD data. That CAD geometry is divided up into small units (spatial discretization). In 3D the units frequently correspond to hexahedrons or tetrahedrons. Various states are calculated in the simulation for those units, more specifically piecewise in small time units (temporal discretization). Various equations are solved in each time unit, for example the continuity equation or the Navier-Stokes equation. Process variables of the modeled plastic like for example its temperature, pressure or density can correspond to the states.
The full 3D model gives the most accurate results, but is also the most time-intensive and processing-intensive. Simplifications to the full 3D model form the Hele-Shaw model (the geometry is described by a plane, to each location of which a wall thickness is attributed), the 2.5D model or the dual-domain model.
Particularly in connection with full 3D models, the spatial discretization per se does not have to be static but can also change with the progression in the simulation (adaptive grid definition). In that way, the computing accuracy can possibly be increased and the computing time possibly reduced.
Temporal discretization typically arises out of establishing a so-called courant number Co which specifies by how many cells a variable (typically the plastic mass) advances at a maximum per time step. An individual time step or calculation step therefore involves in the process a corresponding duration (for example 10 μs<Δt <10 ms) and that process duration is generally different for each time step. Accordingly, temporal discretization is conditioned by the respective cell sizes, the respective flow speeds and the defined courant number. That can be a number between 0 and 1 (0<Co<1) or once again a function 0<Co(x)<1, wherein x denotes most widely varying dependencies (time, location, pressure, combinations and so forth).
The higher the degree of spatial discretization (the respectively smaller the cells), the higher the flow speeds and the lower the courant number, the correspondingly less is the process duration being implemented in a respective calculation step. The smaller the respective process durations of the respective calculation steps, the correspondingly more calculation steps are required to conclude a filling operation. The computing resources for a calculation step are approximately independent of the respective process duration. Accordingly, the computing resources required in total rise with a higher degree of spatial and temporal discretization.
Enlarged Injection Molding Simulations
The geometry of the cavity can be enlarged by that of the nozzle, the hot runner system, the distributor, the screw pre-chamber and so forth. Many simulations also take account of the complete tool and the temperature conditioning passages disposed therein.
The depicted physics in the simulation can also include crystallization of polymers, or orientation and thermal damage to fillers. Heat transfer, shearing speed- and pressure-dependent viscosity, shearing heating, freezing of edge layers and so forth also play a part. Then or parallel to filling/injection molding simulations it is also usual to carry out temperature conditioning, cooling, distortion or shrinkage analysis operations.
Simulations for Process Optimization
Injection molding simulations are typically used in tool construction for the following tasks: determining orientation of fibers; avoiding weld seams; determining the necessary closing force; dimensioning wall thicknesses; optimizing position, number and size of gatings; minimizing distortion; determining demoldability; avoiding hotspots; calculating the filling time; determining shrinkage; determining sink marks; avoiding venting problems; and determining internal stresses.
In the meantime, the complicated and expensive but accurate 3D-FEM simulations are also being used for realistic calculation of the injection molding process in order moreover to permit offline optimization of conditions or the machine setting (input parameters). In that respect, the filling speed/filling time, melt or tool temperatures or the post-pressure level are to be optimized. Higher-order optimization aims are a robust injection molding process, a short cycle time or a molding surface without defects like for example sink marks, streaks or burns.
For optimization purposes, statistical experiment planning (English: Design of Experiments—DoE) is used in practice. For DoE, the operator of a simulation software normally (manually) defines a parameter range comprising parameters to be varied (factors) and associated parameter values (levels). The data or results of each filling simulation are analyzed. Required for that purpose are suitable quality functions which depict the results of the simulations on quality variables or make quality-deciding molding or process properties from simulated quantities.
In order to acquire maximum information about the influences and the relationships between the various parameters and to achieve the optimization aims in the best possible fashion, the parameter range should be as large as possible and as far as possible and each combination of parameter values should be analyzed. Obviously, the number of required filling simulations can very easily become very high. Therefore, the number of necessary runs is normally cleverly limited at the expense of the information obtained. Nonetheless, the required simulation involvement remains considerable.
According to the state of the art, multiple simulations are carried out in accordance with the experiment design set up. The results are respectively analyzed and the relationships between the various parameters and the quality functions are modeled. A (local/provisional) optimum can then be determined. If necessary, or if the required quality criteria could no longer be met within the parameter range covered, new/other parameter ranges are used in further iterations. That lifts it to an “optimum”.
Various supporting/alternative algorithms were devised in the literature and vividly summarized by Yang et al 2015 in FIG. 1 (reproduced in adapted form) (see Yi Yang, Bo Yang, Shengqiang Zhu, Xi Chen. Online quality optimization of the injection molding process via digital image processing and model-free optimization. Journal of Materials Processing Technology 226 (2015) 85-98). For the present invention, it is primarily that identified as “offline” and specifically the use of “first principle models”, that is relevant. A combination and alternate use of other methods is however certainly possible.
Following the various simulations or first principle models, CFD- and FEM-calculations and so forth, the results thereof are analyzed. After implementation and analysis of a (one-factor-at-a-time) simulation or a plurality of (DoE) simulations, a check is made as to whether the quality criteria are met and in turn that is followed by the decision as to whether and which parameters can/are to be possibly modified in a further iteration. That procedure in the state of the art is illustrated in FIG. 2 from EP 1 218 163 B1.
A flow chart of offline process optimization by injection molding simulations (CFD) in accordance with the state of the art is shown in FIG. 3. The expert knowledge is present in the form of knowledge of an operator and the inputs thereof. The assessment of a simulation is effected, as mentioned, after the end thereof, followed by a check as to whether the results correspond to the quality requirements. Parameters or conditions are possibly modified and a further simulation is carried out.
A process which is improved over that procedure is state of the art and is shown in FIG. 4. Instead of iteratively modifying the parameters or conditions, with the aim of achieving optimum simulation results, an experiment plan (DoE) is prepared. That is processed, each of the simulation results is assessed, possibly modeling is effected and an optimum is identified. Optionally that procedure can be combined with the above “iterative optimizer” (FIG. 3).
For example EP 1 218 163 A1 or US 2008 0294402 disclose methods of the general kind set forth for the simulation of an injection molding process.